\section{Conclusion}
\label{conc}

In this paper, we introduce a novel {\em path-tree} structure to assist the compression of transitive closure and answering reachability query. 
Our path-tree generalizes the traditional tree cover approach and can produce better compression rate for the transitive closure. 
We believe our approach open up new possibilities for handling reachability query for large graphs. 
Path-tree also has the potential to integrate with other existing methods, such as Dual-labeling and GRIPP, to further improve the efficiency of reachability query processing. 

